Confused by nonlocal models and relativity

[DarMM]

Well let's make it simpler. You understand the sense in which $E$ is taken to describe an actual propogating physical system?

 

[martinbn]

Well let's make it simpler. You understand the sense in which $E$ is taken to describe an actual propogating physical system?

Yes.

 

[DarMM]

Then saying $\psi$ is real is a shorthand for saying that $\psi$ is similarly describing an actual propogating physical system.

As opposed to $\psi$ just describing the probabilities of various outcomes.

 

[martinbn]

Then saying $\psi$ is real is a shorthand for saying that $\psi$ is similarly describing an actual propogating physical system.

As opposed to $\psi$ just describing the probabilities of various outcomes.

That's is what I thought initially. But it makes no sense to me to say that $\psi$ an actual propagating physical system. Because the domain on which it is defined is not space-time. If you have more than two particles how do you makes sense of it?

 

[DarMM]

That's is what I thought initially. But it makes no sense to me to say that $\psi$ an actual propagating physical system. Because the domain on which it is defined is not space-time. If you have more than two particles how do you makes sense of it?

Oh I see. Yes, you run into problems like this once you say $\psi$ is real. It depends on the interpretation how exactly you get out of this. Some versions of MWI for example say that spacetime is simply an illusion caused by decoherence and only $\psi$ exists. I'm sure proponents of the various views can give details.

I myself have difficulty with $\psi$ being real. It literally is a mathematical generalization of a probability distribution, obeys theorems corresponding to a probability distribution, collapse is a generalization of Bayesian updating mathematically. It even obeys a de Finetti type theorem. Why a physical "wave" would obey de Finetti's theorem I find hard to understand.

 

[atyy]

I think it is relevant. The usual understanding is that if the cut is subjective then you get contradictions from extended Wigner's Friend scenarios. If the cut is objective then you have Many-Worlds, just we also have a non-relativistic covariant degree of freedom defined over all of space which specifies where the worlds "stop". So it's either inconsistent or MWI + nonlocal degree of freedom.

Well, but what if Wigner's Friend scenarios are impossible, because you never shift the cut once you make it.

There are other problems with textbook QM + $\psi$ directly describing a physical degree of freedom (Dirac-Von Neumann) unlike textbook QM + $\psi$ as a book keeping device for probabilities (Copenhagen). It's not really an interpretation anybody in Foundations holds to anymore.

But it is consistent if naive, and it is discussed in the paper https://arxiv.org/abs/0706.2661 by Harrigan and Spekkens that proposed the psi-ontic/psi-epistemic definitions that have been widely used. There he calls it ψ-complete.

"It will be useful for us to contrast hidden variable models with the interpretation that takes the quantum state alone to be a complete description of reality. We call the latter the ψ-complete view, although it is sometimes referred to as the orthodox interpretation."

"Specifically, we show that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem. "

"Nonetheless, even if one ignores the non-separability of entangled quantum states, it is straightforward to showthat the manner in which such states are updated after local measurements implies a failure of local causality if one adopts a ψ-complete model "

 

[DarMM]

Oh certainly it is discussed in Spekkens paper there, I don't deny that. However those papers pre-date the extended Wigner's friend cases. It's also not an interpretation that is really held by anybody.

I'll say more soon, just want to look at some notes.

 

[Elias1960]

I think I am not asking my question clearly. I just want to know the definitions of the two different causalities that you use. Einstein causality and signal causality. What has to be concluded by Bell's theorem is a separate question.

To define causality seems too complex for a forum post. All you can expect is some short, sloppy description of the most important aspects.

Signal causality: You have something a human being can influence by his free decision, let's denote this with A. We have something which can be observed, denoted by B. If $P(B|A) \neq P(B)$, then we are able to send a signal from A to B. This concept of causality is completely positivistic, that there exist some causal connection $A\to B$ can, at least in principle, be proven by explicitly sending a signal. Moreover, to name this "causality" is essentially misleading because it is well-defined in a world without any causality in the usual meaning of the word, all that is used here is probability theory (if a signal-causal relation exists follows from some fact about observable probabilities). Ok, some notion of free will or at least some independence of the decisions of experimenters, to define the difference between what the experimenter is doing at A (making a decision what to send to B) and what the observer is doing at B (observing what should contain A's message).

Classical causality: I have no simple list of axioms, simply because I have not tried to find one. The conceptual difference is quite big, causality is a different structure of the world which is not directly observable, but what is supposed to explain what we observe in a non-mystical way. Causal explanations are always theoretical, hypothetical explanations, and go beyond what they are supposed to explain. "Signal causality" is, in this sense, no causality at all, but, instead, simply a description of some observation.

Important properties of causal explanations are: 1.) There is no causal influence into the past. As a consequence (and in situations where "the past" is not well-defined by observation) there are no causal loops. 2.) The axioms of a partial order relation. 3.) Free will decisions or at least variants of them (combining dice throwing, a free-will decision, a deterministic random number generator, some random quantum effect, and characteristics of light coming from different ends of the universe by some well-defined algorithm into a single decision) do not have a cause (no superdeterminism). 4.) And, of course, particular causal influences should correspond to what follows from the scientific laws, in particular, the laws of physics, forbidding most of the astrological "causal" influences (but not all, the date of birth has a lot of influence on weather and so on in the first year of life, which can have, at least in principle, a lot of influence on character-forming and so on).

But the most important thing is what makes a causal explanation a necessity, or a missing causal explanation an open scientific problem. Without such a necessity, causality could be simply ignored. The "but this has no explanation" could be answered by a simple "so what?". And here the key principle is Reichenbach's principle of common cause. Every nontrivial correlation requires a causal explanation.

Einstein causality I have not even mentioned, because it comes in those two variants too.

 

[atyy]

Oh certainly it is discussed in Spekkens paper there, I don't deny that. However those papers pre-date the extended Wigner's friend cases. It's also not an interpretation that is really held by anybody.

Well, what to me seems unintuitive about what you are saying is that you seem to be saying that the minimal interpretation requires one to believe that psi is not real, whereas typically we say that the minimal interpretation is agnostic.

Also, I don't understand why the extended Wigner friend scenarios have anything to do with it. I thought we agreed the papers don't make sense from a Copenhagen viewpoint. And from a Copenhagen viewpoint, it doesn't seem as if one has to to be committed anyway to the reality or non-reality of the wave function. Maybe just think of it as two levels of reality. There is the outer reality, and the inner reality which is just a tool to compute the probabilities of measurement outcomes, the latter part being exactly the same as a version of Copenhagen where the wave function is not real.

I suspect that what you are saying is that the minimal interpretation cannot emerge from Bohmian Mechanics by definition.

 

[DarMM]

Well, what to me seems unintuitive about what you are saying is that you seem to be saying that the minimal interpretation requires one to believe that psi is not real, whereas typically we say that the minimal interpretation is agnostic.

No, for example you might leave open that Bohmian Mechanics and MWI are true.

Also, I don't understand why the extended Wigner friend scenarios have anything to do with it. I thought we agreed the papers don't make sense from a Copenhagen viewpoint. And from a Copenhagen viewpoint, it doesn't seem as if one has to to be committed anyway to the reality or non-reality of the wave function

They make sense, they just don't invalidate Copenhagen. $\psi$ not being real is a fundamental part of the Copenhagen view in any exposition of it I've read. Either in the writings of Bohr, Heisenberg, Pauli, Peierls or more modern papers or courses like Matt Leifer's.

 

[Elias1960]

I agree with this provided one leaves room for the possibility that the current formal mathematical logic can be extended to a more general one for physical theories if at some point experiments lend themselves to a more comprehensive form of scientific theory. This is of course not my idea but was contemplated by people like Poincaré, Weyl and Brouwer.

In principle, indeed, I would not completely exclude the possibility that some empirical facts could influence the laws of reasoning.

Last but not least, our ability of reasoning is the result of evolution, which means, it is useful for our survival, but this usefulness is based on the quite small domain of circumstances that are important for the survival of humans and their predecessors. This classical argument is not without any value. At least in principle one cannot exclude the possibility that some completely strange observations made in a domain inaccessible to our predecessors could force us to modify even our laws of reasoning.

But this would require much more otherwise unexplainable evidence. In the actual world of modern physics, there is essentially nothing in contradiction with common sense at all, at least if one allows common sense compatible explanations of modern physics to be discussed (thus, not in this forum, which forbids to discuss even the original interpretation of SR). Everything in modern physics is compatible even with Newtonian/Kantian understanding of absolute space and time (with relativistic effects explained by a distortion of clocks and ruler by the gravitational field) and a completely classical ontology where the wave function described only our incomplete knowledge about the real configuration of the quantum system and the world around it. If even a rejection of classical spacetime theory and classical ideas about the ontology depend on heavy metaphysical decisions against common sense, there is no base for even questioning the laws of reasoning, which are yet on another, higher level.

Indeed, common sense would have no problem with accepting that Newtonian absolute space and time are simply wrong. Not even this is certainly falsified by any empirical evidence, theories which accept a Newtonian spacetime and explain relativistic effects by distortions of rulers and clocks exist, they even give the Einstein equations in some natural limit, thus, are quite plausibly viable.

Similarly for the quantum part. Common sense has no problem with accepting that beyond the classical configuration there is something more, say, some wave function, which really exists. But not even this follows from any experimental evidence. Caticha's entropic dynamics gives a completely classical picture of what really exists (the same as in a classical Lagrangian picture, a trajectory in the configuration space), and the wave function is, together with the Schroedinger equation, derived from entropic inference, as a function which describes simply our incomplete knowledge about the quantum system.

So, modern physics has viable interpretations which are compatible not only with the classical laws of reasoning (in their modern understanding, classical logic together with the logic of plausible reasoning) but even with old Newtonian absolute space and time as well as a completely classical ontology as used in the Lagrange formalism.

That means, while in principle I would acknowledge that a world where empirical evidence forces us to modify even the laws of reasoning, the actual world of modern physics is far away from such a situation.

Spoiler: What is missed in physics is the counterrevolution after the revolution

All revolutions in the political area have, after some time, experienced some sort of counterrevolution, sometimes explicitly, sometimes simply by the new elites silently reviving useful and necessary things which have been destroyed during the revolution.

Kuhn describes science in terms of having revolutions too. The characteristic of those scientific revolutions is that everything can be questioned. But, once the revolution was successful and a new theory found, what about all the things which have been unjustly questioned and rejected? If science would be a rational endeavor, it would be reasonable to try to revive them. Thus, given that it is unknown what has been rejected without justification, one should have tried to revive everything that has been rejected during the revolution. There would have been ideas that could be revived, and ideas where the revival appeared to be impossible. But this was not done.

To question everything during a scientific revolution is fine, adequate, justified. But once the revolution was successful, and the new theory was found, a similar counterrevolution has to start, which tries to make everything which has been rejected during the revolution compatible with the new theory. And this counterrevolution is completely missed. The scientific analogon of Jacobin terror continues up to now.

 

[atyy]

No, for example you might leave open that Bohmian Mechanics and MWI are true.

Well, perhaps we use the word interpretation in a different way. How about minimal formalism instead of minimal interpretation. To me, I would say that the minimal formalism emerges from BM, and that within the minimal formalism it is consistent to treat the wave function as real, but complete within the formalism - although it is incomplete from the point of BM. It is complete in the sense of completeness for the purpose of making predictions of the probabilities of measurement outcomes.

They make sense, they just don't invalidate Copenhagen. $\psi$ not being real is a fundamental part of the Copenhagen view in any exposition of it I've read. Either in the writings of Bohr, Heisenberg, Pauli, Peierls or more modern papers or courses like Matt Leifer's.

I would more typically say that there is neither a commitment to the wave function being real or not real. I think it is the meta-rule of Copenhagen that you must first set up the cut before you do anything else, and that you don't move the cut, that makes the extended Wigner friend scenarios irrelevant for Copenhagen. As long as you don't move the cut, it doesn't matter whether you think the wave function is real or not.

 

[DarMM]

Well, perhaps we use the word interpretation in a different way. How about minimal formalism instead of minimal interpretation. To me, I would say that the minimal formalism emerges from BM, and that within the minimal formalism it is consistent to treat the wave function as real, but complete within the formalism - although it is incomplete from the point of BM. It is complete in the sense of completeness for the purpose of making predictions of the probabilities of measurement outcomes.

I'm not sure I fully follow, but the wavefunction of minimal QM comes from the Bohmian epistemic $\psi$ not the fundamental $\Psi$ of Bohmian Mechanics. This distinction matters in Frauchiger-Renner type scenarios.

I would more typically say that there is neither a commitment to the wave function being real or not real

I don't agree with this. Bohr, Heisenberg, Pauli, Peierls and many others explicitly state the wave-function is just a catalogue of probabilities. More modern Copenhagen people say this. It's what's said about Copenhagen in the Perimeter Institute's Quantum Foundations courses no matter who teaches it each year.

See slide 11 here:
http://mattleifer.info/wordpress/wp-content/uploads/2018/05/Lecture26.pdf

 

[vanhees71]

I am guessing I don't know what degree of freedom is. It is intuitive in mechanics. A point in the plane has two degrees of freedom. In electrodynamics the electric field has infinitely many degrees of freedom. But wouldn't have thought that the field itself is called a degree of freedom.

I'm also lost. Now the apparently clear notion of "physical degree of freedom" is also blurred by philsophical unclear redefinitions.

In physics there are two kinds of "degrees of freedom", applying either to point-particle mechanics, where it is described as a finite number of independent configuration-space variables $q^k$ with $k \in \{1,\ldots f \}$, or field-degrees of freedom. E.g., the electromagnetic field is described by 6 field-degrees of freedom, e.g., the 3 electric and the 3 magnetic field components.

Now they start to claim that the quantum mechanical wave function $\psi$ is a "degree of freedom". What should that mean? The important point is that first of all this applies only to non-relativistic QM, where a single wave function makes sense as the representative of a $N$-paticle system with a fixed number of particles. It's a function of time and configuration space $(\vec{x}_1,\ldots,\vec{x}_N)$ and not a field to begin with. Also its meaning is very clear: $|\psi|^2$ is the probability density for the $N$-particle system to be in configuration space at $(\vec{x}_1,\ldots,\vec{x}_N)$ when measured at time, $t$. I don't see any way, which sense it should make to declare the wave function to be a "degree of freedom". This was a very early idea by Schrödinger, which was almost immediately given up, which made Schrödinger in fact very upset, but he had to give in finally, since there's no sensible way to define the wave function as some kind of field.

In relativistic physics since the particle number is not conserved (which is an empirical fact) you cannot use wave functions to begin with but have to introduce quantized fields. So far the only successful kind of QFTs are those with local interactions, i.e., using realizations of the proper orthochronous Poincare group using field operators which admit to define local observables which obey the microcausality constraints, which is realized by using fundamental field operators obeying either canonical equal-time commutator (bosons) or anticommutator (fermions) relations. Sometimes one talks sloppily about these quantized fields in terms of "field-degrees of freedom" though this is kind of misleading either. At least fermion fields are hard to interpret classically at all. From the path-integral formalism we know that such fields should be Grassmann valued functions, but what this should physically mean as a classical field theory, i.e., not as a calculational tool to evaluate fermionic path integrals, is not clear at all.

 

[akvadrako]

Why a physical "wave" would obey de Finetti's theorem I find hard to understand.

I don't know about Finetti's theorem specifically, but I suspect the connection between objective reality and probability theory is something like this: breaking the rules of probability is forbidden logically because it would lead to an inconsistency, i.e. probability should include everything possible. Perhaps the universe has the same set of restrictions. I was reminded of this idea in a recent paper by Adán Cabello, The problem of quantum correlations and the totalitarian principle.

This result fits with Wheeler’s thesis that the universe lacks of laws for the outcomes of some experiments and with Born’s intuition that quantum theory is a consequence of the non-existence of ‘conditions for a causal evolution’

 

[DarMM]

I'm also lost. Now the apparently clear notion of "physical degree of freedom" is also blurred by philsophical unclear redefinitions.

In physics there are two kinds of "degrees of freedom", applying either to point-particle mechanics, where it is described as a finite number of independent configuration-space variables $q^k$ with $k \in \{1,\ldots f \}$, or field-degrees of freedom. E.g., the electromagnetic field is described by 6 field-degrees of freedom, e.g., the 3 electric and the 3 magnetic field components.

Now they start to claim that the quantum mechanical wave function $\psi$ is a "degree of freedom". What should that mean?

Basically they mean it's like a field degree of freedom on a higher dimensional space (configuration space). As you said, yes this is basically what Schrodinger originally thought and yes like you I have literally no idea what it could mean in QFT.

 

[atyy]

I'm not sure I fully follow, but the wavefunction of minimal QM comes from the Bohmian epistemic $\psi$ not the fundamental $\Psi$ of Bohmian Mechanics. This distinction matters in Frauchiger-Renner type scenarios.

Ah that is an interesting point. I have never understood what the proper classification of the various Bohmian psis are. @Demystifier has explained this to me several times, but I have not understood it well enough to have the answer off the top of my head. I presume in this case you don't mean that the Bohmian epistemic psi is "psi-epistemic" in the Harrigan and Spekkens sense?

I don't agree with this. Bohr, Heisenberg, Pauli, Peierls and many others explicitly state the wave-function is just a catalogue of probabilities. More modern Copenhagen people say this. It's what's said about Copenhagen in the Perimeter Institute's Quantum Foundations courses no matter who teaches it each year.

Yes, but earlier you mentioned Dirac-von Neumann. Now I doubt that Dirac and von Neumann were any less sophisticated than Bohr or Peierls, but just to use your terminology, it does indicate that there is an idea that within the conventional formalism that the wave function cam be considered nonlocal. Apart from the Harrigan and Spekkens paper, one can see this attitude in https://arxiv.org/abs/0706.1232 (Fig. 1) and https://arxiv.org/abs/quant-ph/0209123 (p51) "In other words, even if one can discuss whether or not quantum mechanics is local or not at a fundamental level, it is perfectly clear that its formalism is not ..."

So what I understand this view to be is it is Copenhagen, and it starts off with the wave function is just a catalogue of probabilities, but it adds: "the wave function is just a catalogue of probabilities because of some obvious absurdities like collapse if it is real. Nonetheless, from an operational point of view we don't need to decide on the reality of the wave function to proceed with using the formalism, so we set up the cut and state and quantum formalism. At the point of usage, since we believe it makes no operational difference whether the wave function is real or not, we can use the mental picture of a real wave function to help with calculations, ie. reality is a tool to predict the probabilities of measurement outcomes." Since the reality of the wave function only enters at the last stage, I think it has enough of Copenhagen to be protected from the extended Wigner friend scenarios.

 

[DarMM]

Now I doubt that Dirac and von Neumann were any less sophisticated than Bohr or Peierls

It's not so much named after them to indicate it's their view, but that it's what one might naively think from reading the axioms that first appear in their texts. von Neumann didn't himself think of $\psi$ as an actual real field and Dirac is fairly explicit in thinking $\psi$ is just a collection of probabilities.
Regardless in modern usage in papers and books, Copenhagen is taken to have as a defining element the view that $\psi$ is not a real propogating field but just a collection of statistics.

I'll respond to the rest tomorrow.

 

[Demystifier]

Ah that is an interesting point. I have never understood what the proper classification of the various Bohmian psis are. @Demystifier has explained this to me several times, but I have not understood it well enough to have the answer off the top of my head. I presume in this case you don't mean that the Bohmian epistemic psi is "psi-epistemic" in the Harrigan and Spekkens sense?

A short reminder. Suppose that a closed system contains two particles. Then its wave function is $\Psi({\bf x}_1,{\bf x}_2,t)$ and always satisfies the Schrodinger equation. The wave function of the open subsystem, e.g. the wave function of the first particle, is then
$$\psi({\bf x}_1,t)=\Psi({\bf x}_1,{\bf X}_2(t),t)$$
where ${\bf X}_2(t)$ is the Bohmian trajectory of the second particle. The wave function $\psi({\bf x}_1,t)$ does not always satisfy Schrodinger equation.

 

[vanhees71]

What's the physical meaning of $\psi(\mathbf{x}_1,t)$ then?

 

[Demystifier]

What's the physical meaning of $\psi(\mathbf{x}_1,t)$ then?

Suppose that $\mathbf{X}_2$ is not a position of a single microscopic particle, but a collective position of a macroscopic pointer in the measuring apparatus. In other words, suppose that $\mathbf{X}_2$ is a position that we can directly perceive (a perceptible, in the language on my paper). Then $\psi(\mathbf{x}_1,t)$ is the wave function that we associate with the first particle when we know the position of the pointer. This is what, in standard QM, corresponds to the update of wave function (which some people like to call "collapse", but we both agree that there is no true collapse) given a knowledge provided by the measuring apparatus. In this way, Bohmian mechanics explains what standard QM takes for granted, namely that a macroscopic pointer has a position and that knowledge of this position can be used to update the wave function.

 

[vanhees71]

Interesting, and what's the formal justification for this interpretation?

 

[Demystifier]

Interesting, and what's the formal justification for this interpretation?

One justification is the fact that in this way one can reproduce the standard textbook "collapse" rule (which correctly predicts probabilities of subsequent measurements), without having an actual collapse. It is explained in more detail in the book on Bohmian mechanics by Durr et al that you read.

Or perhaps you would like a different type of justification?

 

[A. Neumaier]

Suppose that $\mathbf{X}_2$ is not a position of a single microscopic particle, but a collective position of a macroscopic pointer in the measuring apparatus. In other words, suppose that $\mathbf{X}_2$ is a position that we can directly perceive (a perceptible, in the language on my paper). Then $\psi(\mathbf{x}_1,t)$ is the wave function that we associate with the first particle when we know the position of the pointer. This is what, in standard QM, corresponds to the update of wave function (which some people like to call "collapse", but we both agree that there is no true collapse) given a knowledge provided by the measuring apparatus. In this way, Bohmian mechanics explains what standard QM takes for granted, namely that a macroscopic pointer has a position and that knowledge of this position can be used to update the wave function.

And what is the particle's wave function before the measurement?

 

[Demystifier]

And what is the particle's wave function before the measurement?

Before the measurement we usually assume that there is no entanglement, in which case there is no important difference between $\Psi$ and $\psi$. Does it answer your question?

 

[A. Neumaier]

Before the measurement we usually assume that there is no entanglement, in which case there is no important difference between $\Psi$ and $\psi$. Does it answer your question?

One cannot assume this when one only has the Bohmian dynamics, unless one assumes that the universe was created at the time of the preparation of the experiment. This can be seen by running the Bohmian mechanics backwards from your assumed condition - it will be unentangled only for an instant.

In contrast, Copenhagen does not claim to model the whole universe but only the small system between preparation and measurement, hence can make initial assumptions without running into a contradiction.

 

[vanhees71]

Usually you assume that before the measurement, i.e., the interaction between the measured system and the measurement device these are unentangled, which makes sense since the preparation of the system and the device before the measurement should be independent to have a defined distinction between them and a well-defined measurement to begin with.

 

[A. Neumaier]

Usually you assume that before the measurement, i.e., the interaction between the measured system and the measurement device these are unentangled, which makes sense since the preparation of the system and the device before the measurement should be independent to have a defined distinction between them and a well-defined measurement to begin with.

Yes, this is permitted in interpretations that do not claim to derive their dynamics from the dynamics of a bigger system that also involves the preparation and measurement procedure. But Bohmian mechanics is supposed to derive everything from a deterministic dynamics of the universe, hence has no room for additional assumptions unless these can be proved from the deterministic model.

 

[Demystifier]

One cannot assume this when one only has the Bohmian dynamics, unless one assumes that the universe was created at the time of the preparation of the experiment.

One can assume this, of course only in a certain approximative sense. The other important concept in Bohmian mechanics that you are missing is the effective wave function, which explains why most of the entanglement that the subsystem has with the rest of the universe can be neglected.

 

[Demystifier]

hence has no room for additional assumptions unless these can be proved from the deterministic model.

They can be proved, but perhaps not rigorously proved as you would like. See https://arxiv.org/abs/quant-ph/0308039
especially Sec. 5.

 

[A. Neumaier]

One can assume this, of course only in a certain approximative sense.

But you need to show why, in some approximate sense, this assumption is justified by the deterministic theory!

The other important concept in Bohmian mechanics that you are missing is the effective wave function, which explains why most of the entanglement that the subsystem has with the rest of the universe can be neglected.

No. my question was aimed at this, and you had answered with separability. I don't see how the deterministic theory implies separability for the effective wave function.

They can be proved, but perhaps not rigorously proved as you would like. See https://arxiv.org/abs/quant-ph/0308039
especially Sec. 5.

(5.6) assumes that the universal wave function factorizes, an assumption completely unstable under small temporal changes, hence not warranted. They mention this after (5.11); it is strange that they discuss this unrealistic case at all. After (5.8), another unwarranted assumption is made ''that the interaction between the x-system and its environment can be ignored''. But the bigger a system the more entangled it is with the remainder of the universe! And you invoked a big system (consisting of a measured system and its measuring device)!

(5.12) doesn't help as it is questionable whether the entanglement can be described by a few separable summands with essentially disjoint support. That the form (5.15) ultimately assumed is typical for is an unproved assumption that I find quite unlikely to be derivable from the dynamics.

The only mathematically natural definition of an effective wave function for a subsystem consisting of particles in a set S and the complementary set E of particles in the environment is to take the universal wave function $\Psi(x_S,x_E,t)$ and substitute for all environmental particles their Bohmian position $x_E(t)$, i.e., $\psi(x_S,t):=\Psi(x_S,x_E(t),t)$. But is there any theory that this effective wave function would behave in the
Copenhagen way - i.e., according to the Schrödinger dynamics before a measurement is made, and collapsing after the measurement is made? I doubt it...

 

[Demystifier]

That the form (5.15) ultimately assumed is typical for is an unproved assumption that I find quite unlikely to be derivable from the dynamics.

I think it's (non-rigorously) proved from dynamics in the literature on decoherence theory. See e.g. the book by Schlosshauer, Sec. 2.8.4.

 

[A. Neumaier]

That the form (5.15) ultimately assumed is typical is an unproved assumption that I find quite unlikely to be derivable from the dynamics.

I think it's (non-rigorously) proved from dynamics in the literature on decoherence theory. See e.g. the book by Schlosshauer, Sec. 2.8.4.

The subsection ''Selection of Quasiclassical Properties''? This is 2 1/2 pages of prose arguing for preferred emerging pointer states in traditional quantum mechanics (not Bohmian mechanics). I don't see there anything related to (5.15).

Checking back it seems that whatever is done in Section 2.8 is based on the nondemolition assumption - (2.84) on p. 90 - which we had discussed before as being a nontypical special case.

 

[Demystifier]

The subsection ''Selection of Quasiclassical Properties''? This is 2 1/2 pages of prose

This prose contains references to the literature with more details. The purpose of prose in physics, of course, is not to "prove" something but to give intuitive undertstanding.

arguing for preferred emerging pointer states in traditional quantum mechanics (not Bohmian mechanics).

Exactly! The questions you are asking are not related exclusively to Bohmian mechanics. They are equally related to many worlds, decoherence, von Neumann measurement theory, and all related approaches.

I don't see there anything related to (5.15).

If you can read between the lines, you can find it in item 1 at page 84.

Checking back it seems that whatever is done in Section 2.8 is based on the nondemolition assumption - (2.84) on p. 90 - which we had discussed before as being a nontypical special case.

In that discussion before, it seems that you missed my post #70, where I explained mathematically why the ideas work even without the nondemolition assumption.

 

[bhobba]

Basically they mean it's like a field degree of freedom on a higher dimensional space (configuration space). As you said, yes this is basically what Schrodinger originally thought and yes like you I have literally no idea what it could mean in QFT.

Nor do I - but I know of a book with the view QFT can be presented in a 'realistic' way:
https://www.amazon.com/dp/9812381767/?tag=pfamazon01-20

Here is the issue. We believe things like mass, momentum, and energy (remember mass is a form of energy) are real - without going into the issue what real is. IMHO its one of those fundamental things you can't really pin down - others of course will disagree. Anyway by Noether fields are real because they have energy and momentum. But when quantised the field is described by a very abstract thing - quantum operators. Note this is not saying reality is quantum operators - just its described by it. Since classical fields are real, and they are simply a limit of quantum fields, quantum fields must be real. Normal QM is QFT when particles are dilute - but since the fields are real that means normal QM is real. Now since everything is a quantum field the issue is looking at QFT in a way that seems reasonable - and that is what the book attempts to do.

Thanks
Bill